Resonances, Standing Waves and Normal modes of a column of air Detail of a feast for Nebamun, fragment of a scene from the tomb-chapel of Nebamun. Thebes, Egypt, Late 18th dynasty, around 1350BC Props: organ pipe, flute, whirly tube, didgeridoo, slinky, pan flute, ocarinas Big tube, microphone, preamp, speaker and sine generator Tape measure Resonant excitation of tuning fork, string and tube with speaker (if not done in last lecture) One sided Cable to illustrate open boundary condition Slinky for showing longitudinal excitations Heavy cable for showing a different boundary condition in a string Doppler ball, whirly film cartridge with slot wave generator on string + pole (or in previous lecture) If extra time show spectral display with time of liquidnitrogen or the syrinx or the quark song! (or previous lecture) Power point Alice Quillen

from DAVID O'BRIEN WHISTLES review by Jessie Driscoll Wind Instruments Tubes of air excited by blowing vibrations organ pipes, flutes, whistles, recorders brass family, reed instruments didgeridu ocarina demo flute, organ pipe, recorder digi_kanghop.mp3 from DAVID O'BRIEN WHISTLES review by Jessie Driscoll

Pressure waves in air Longitudinal waves Slinky demo Animation from Dan Russel

Standing waves or modes in a column of air The motions shown are air velocity. The shorter wavelength motions should be faster. One of these is a pipe that is closed on one end and the other is open on both ends. Which one is which?

Open/open tube

Open/closed tube

Harmonics or overtones Closed/open tube only has odd harmonics (e.g., clarinet) f, 3f, 5f, 7f Open/open tube has all integer multiples f,2f,3f,4f,5f (e.g., organ pipe) In this case the tubes are the same but the boundary conditions are different. The boundary: A closed end allows large pressures but no motions. An open ends allows motions but no pressure changes. Demo the whirly tube show harmonics AND show that notes are higher when smaller

Music from overtones of pipes Sarah Hopkins Kindred Spirits from Gravikords, Whirlies and Pyrophones sarah_hopkins.mp3 note Doppler shift!

A wave reflecting off of the boundary At an open boundary: the air bounces moving in and out of the boundary. When the air moves out the pressure in the middle is low and the air is sucked back in. When the air moves in, the pressure is high in the middle and the air is pushed back out. Demo boundary conditions with string and cable motions

Wave reflecting off of the closed boundary At a closed boundary: the wave reflects if it has a high pressure at the wall. The air compresses at the wall and then bounces back.

Normal modes of a column open/closed No pressure variation, large motions No motions, large pressure variations

Which one has a lower fundamental tone? Open/open or open/closed? Open/open open/closed closing end of flute!

Length, fundamental and harmonics The open-closed pipe has a fundamental wavelength equal to four times its length and higher resonances at odd integer multiples of the fundamental frequency. The open-open pipe has a fundamental wavelength equal to two times its length and higher resonances which occur at all integer multiples of the fundamental frequency.

Resonant excitation Small pushes correctly timed will add up and excite large amplitude motion. Small pushes incorrectly timed will tend to cancel out.

Resonant excitation of a column of air How long does it take a disturbance to travel down the length of the tube and come back? Correctly timed excitations allow the mode to grow. Otherwise they are cancelled out by each other.

Boundaries Open end A travelling positive pressure pulse pushes the air out converting the pressure pulse into motion. The motion outwards excites a vacuum pulse inside moving the other way and flipping the sign of the pulse --- analogous to the fixed end of a string. Closed end At a closed boundary a high pressure pulse bounces against the boundary sending back a positive pressure pulse. Analogous to the free end of a string.

Waves reflecting off of boundaries russell_hards_wm.gif russell_softs_wm.gif Animations courtesy of Dr. Dan Russell, Grad. Prog. Acoustics, Penn State

Reflection at boundary Sign of wave reflected depends on nature of boundary Show on string, vs cable If the sign is opposite or same then 2 reflections needed to get back to original If sign is opposite on one side and same on other then 4 reflections needed

Open/Closed Open/Open reeds horns digi panflutes flutes organ pipes recorders, whistles

Excitation of digi digiclip.mov movie by me+Raz Rivlis

Which modes will grow? If I put random pressure fluctuations into the pipe, some will grow and others will not. How do I describe the way the pipe reacts to an input sound? Impedance is a way to measure this. Relates input pressure to actual air velocity. Is a function of frequency

Speed of sound and excitation of a mode in an open column of air The speed of sound is 330 m/s If the column is 1.7m long then it takes Demo: on open pipe with microphone to show volume change Find harmonics Demo on closed pipe If the column is excited at this frequency then a resonance is likely to be excited.

Water trumpet analogy for a trumpet From Benade

Timbre of Winds clarinet flute The fundamental for A5 should be around 920Hz. The low frequency in the flute suggests that the lower octave note is also excited. Clips: Britten_Pan clip in Winds, Debussy_Syrinx_clip in Winds Despite closed end clarinet has all integer harmonics Flute has stronger lower harmonic compared to clarinet -- Flute also seems to have some intermediate frequencies from the lower octave.

Clarinet and Brass Clarinet Horn Clip: Blacher_divertimento_1 in Winds Horn has more broad band noise particularly at lower frequencies and at start of note. As was true for the flute there are tones in between but they are not the octave below.

Digderidu clip: digi_kanghop.mp3

Ocarina Pitch adjusted by number of open holes rather than position of hole – not a tube! Almost pure tones ocarina.mp3

vocal track is a squat deformable ~cylinder Whistle vocal track is a squat deformable ~cylinder can I make a better demonstration of this! frequency

Sliding whistle When all the way in, no longer acts like a tube of air. Acts more like an ocarina. Lost of higher harmonics. Noted by many in the lab! Even integer harmonics often weak because of inner closed end.

frequency  time  loudness frequency  Sliding whistle 300Hz 900Hz 1500Hz strong odd integer harmonics weak even integer 600Hz loudness sliding_whistle_2notes.mp3 frequency 

Inside the whistle

Spectrum and resonances On the string, each overtone frequency corresponds to a mode of oscillation In percussion instruments that is also often the case With wind instruments, integer multiple overtones are often seen but these are not always resonances of the instrument

Terms introduced Resonances Resonant excitation Pressure waves Boundary conditions Longitudinal waves Open/open and open/closed tubes and modes of oscillation in them Impedance Spectral display of quark song or liquid nitrogen?

Recommended reading Chap 6 of Hopkin on Aerophones pages 73-75